STATUS
proposed
approved
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Revision History for A236913
(Bold, blue-underlined text is an addition; faded, red-underlined text is aShowing entries 1-10 | older changes
STATUS
editing
proposed
EXAMPLE
This sequence counts even-length partitions of even numbers (, which have Heinz numbers given by A340784). For example, the a(0) = 1 through a(4) = 12 partitions are:
EXAMPLE
These are This sequence counts even-length partitions of 2neven numbers (Heinz numbers A340784). For example, the a(0) = 1 through a(4) = 12 partitions are:
CROSSREFS
Note: A-numbers of Heinz-number ranking sequences are in parentheses below.
The ordered version is A000302.
COMMENTS
From Gus Wiseman, Feb 09 2021: (Start)
Also the number of even-length integer partitions of 2n. For example, the a(0) = 1 through a(4) = 12 partitions are:
() (11) (22) (33) (44)
(31) (42) (53)
(1111) (51) (62)
(2211) (71)
(3111) (2222)
(111111) (3221)
(3311)
(4211)
(5111)
(221111)
(311111)
(11111111)
(End)
EXAMPLE
From Gus Wiseman, Feb 09 2021: (Start)
These are even-length partitions of 2n. For example, the a(0) = 1 through a(4) = 12 partitions are:
() (11) (22) (33) (44)
(31) (42) (53)
(1111) (51) (62)
(2211) (71)
(3111) (2222)
(111111) (3221)
(3311)
(4211)
(5111)
(221111)
(311111)
(11111111)
(End)
COMMENTS
From Gus Wiseman, Feb 09 2021: (Start)
Also the number of even-length integer partitions of 2n. For example, the a(0) = 1 through a(4) = 12 partitions are:
() (11) (22) (33) (44)
(31) (42) (53)
(1111) (51) (62)
(2211) (71)
(3111) (2222)
(111111) (3221)
(3311)
(4211)
(5111)
(221111)
(311111)
(11111111)
(End)
MATHEMATICA
Table[Length[Select[IntegerPartitions[2n], EvenQ[Length[#]]&]], {n, 0, 15}] (* Gus Wiseman, Feb 09 2021 *)
CROSSREFS
Cf. A000041, A027193, A236559, A160786, A236914, A027187, A027193, A000041.
Note: A-numbers of Heinz-number sequences are in parentheses below.
The case of odd-length partitions of odd numbers is A160786 (A340931).
The Heinz numbers of these partitions are (A340784).
A027187 counts partitions of even length/maximum (A028260/A244990).
A034008 counts compositions of even length.
A035363 counts partitions into even parts (A066207).
A047993 counts balanced partitions (A106529).
A058695 counts partitions of odd numbers (A300063).
A058696 counts partitions of even numbers (A300061).
A067661 counts strict partitions of even length (A030229).
A072233 counts partitions by sum and length.
A339846 counts factorizations of even length.
A340601 counts partitions of even rank (A340602).
A340785 counts factorizations into even factors.
A340786 counts even-length factorizations into even factors.
Cf. A026424, A257541, A300272, A326837, A326845, A340385 (A340386), A340604.
STATUS
approved
editing
STATUS
proposed
approved